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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<a NAME="E1:68"/><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="group_4.html#E96"><i><font color="Green">Lemma49</font></i></a></i>;<br/>
<a NAME="E2:68"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="group_4.html#E96"><i><font color="Green">Lemma49</font></i></a></i>;<br/>
<a NAME="E3:68"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="group_2.html#M1">Subgroup</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>4</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="group_4.html#E96"><i><font color="Green">Lemma49</font></i></a></i>;<br/>
<a NAME="E4:68"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>4</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_2.html#T65">GROUP_2:65</a></i>;<br/>
<a NAME="E5:68"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>4</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
;<br/>
<a NAME="E6:68"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is    <a href="group_2.html#M1">Subgroup</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font>
 
;<br/>
<b>hence </b><a NAME="E7:68"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_2.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="group_4.html#E1:68"><i><font color="Green">E51</font></i></a>, <a class="ref" href="group_2.html#T64">GROUP_2:64</a></i>;<br/>


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